Mathematics College

what are all values of x for which the series shown converges? ​

What Are All Values Of X For Which The Series Shown Converges?

Answers

Answer 1

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}[/tex]

We can write this as:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}[/tex]

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}[/tex]

Then we have the inequality

[tex]1 > (x - 2)/3[/tex]

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

Related Questions

A wizard-in-training has 300 grams of 20% liquid-gold solution. He wishes to drain some and replace it with an 80% solution, so that he gets 300 grams of 35% solution. How many grams should the wizard drain and replace with 80% solution?

Answers

Answer:

it would take 4 grams. I hope this helps

Answer:

75 grams! hope this helps :3

Please help I’ll mark u <3

Answers

Answer:

x>-4

Step-by-step explanation:

Black friday sale on TVs were 50 in tv for $148.00 or 65 in for $199.00 which is the better buy this is not worth a grade just some understanding​

Answers

Answer:

i personally think the 65 in. one

Step-by-step explanation:

a bowling alley charges $4.00 per game and will rent a pair of shoes for $2.00 for any number of games. The bowling alley has an earnings goal of $400 for the day. write the linear equation.

Answers

Answer:

We need 130 games to reach the goal

Step-by-step explanation:

What is the range in interval notation?

Answers

Answer:

The blue box

Step-by-step explanation:

Youre talking about range which takes place on the y-axis (domain is the x-axis).

The top point is an open circle which indicates in the math world the parentheses and the bottom point 1 in a bracket as its a closed circle.

There is a proportional relationship between time in hours and time in days.

A. What is the constant of proportionality?

B. what equation describes this relationship?

Answers

Of the proportional relationship between time in hours and time in days, we have that:

a) The constant of proportionality is 24.

b) The equation is [tex]h = 24d[/tex].

What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

[tex]y = kx[/tex]

In which k is the constant of proportionality.

Item a:

A day has 24 hours, hence the constant of proportionality is 24.

Item b:

Considering the time in hours as the output and the time in days as the input, the equation is:

[tex]h = 24d[/tex]

You can learn more about proportional relationships at https://brainly.com/question/25815502

Choose the diagram that correctly represents the ordered pairs below.
(1,4), (4, -1), (2,3), (-3, 1), (0,-5)

Answers

Answer:

Step-by-step explanation:

Is there a picture

I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS FIRST

Answers

This is VERY VERY simple! Find the rule. Multiply the individual cost by x. You should be able to find the answer from there... for the last row, multiply your individual cost by 13.

Guys I need some help

Answers

The answer is c your welcome

Solve the system by graphing 3x+y=4 and x-y=4

Answers

Attached is a pic of the graph

Find the greatest common factor of 6 and 35

Answers

Answer:

6

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Find the unit rate. Round to the nearest hundredth, if necessary.

$5.99 for 18 lb

The unit rate is ?/b

Answers

the answer for this is 3.0

part two thinking a number between 1 and 10 but doble the money!

Answers

The answer is 5 dhrnrhenebbebdbrhebrjrn

if f(x) = x^2 + x , find f(-3) a)-12 b)3 c)6

Answers

C is the answer
(-3)^2=9
9+(-3)=6

Please explain how to do this please show work

Answers

Answer:

(x-1)(x+4)

I.e x(x+4)-1(x+4)

Xsquare +4x -x -4

Xsquare +3x -4

pamela ran 7/10 miles on tuesday and 3/8 mile on thursday. How much farther did she sun on tuesday ?

Answers

Answer:

she ran 0.325 more on tuesday then tursday

Step-by-step explanation:

because i know


If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?

Answers

Step-by-step explanation:

Given: Radius , r =21 cm

The angle at the center of the circle, n° =140°

Length of an arc =?

W.K.T Formula, Length of an arc = 2πr( n°÷360°) units

= 2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Answer:

2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Step-by-step explanation:

A table of values of a linear function is shown below.

Answers

Answer:

Slope is -2

y intercept is -3

Equation :y=-2x-3

Step-by-step explanation:

"Individuals, cultures, societies, and the world change through times of conflict and cooperation."
The statement above exemplifies the era of global expansion and encounter. What other word also reflects this theme?
Technology
Trade
Monopoly
Hegemony

Answers

I would say hegemony
Hegemony because it encompasses dominance in which cultures typically dominate over one another creating a popular culture.


By the Exterior Angle Theorem, which of the following is a true statement?

Answers

Answer:

2nd option is the correct answer

Step-by-step explanation:

[tex]m \angle 1 > m \angle 3 \: \& \: m \angle 1 > m \angle 7 \\ [/tex]

According to the Exterior Angle Theorem, the true statement should be considered as the option b.

What is an Exterior Angle Theorem?

The exterior angle theorem defined that at the time when a triangle's side should be extended, the resultant exterior angle formed should be equivalent to the sum of the measures of the two opposite interior angles of the triangle.

So based on this, we can say that the option b is correct.

learn more about an angle here: https://brainly.com/question/6150811

A and B are independent events.
P(A) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
O B. 0.6
O C. 0.4
D. Not enough information

Answers

Answer:

Not enough information

Divide: 1.98 divided by 0.09

Answers

the answer would be 22 :)
The answer is 22 :) hope this helps

Who is good at math?

Answers

Answer:

me depending on what kind of math it is

Step-by-step explanation:

multiple of 3 and 5 less than 47 but greater than 42....​

Answers

Answer:

45

Step-by-step explanation:

45 > 42 but < 47 and it's a multiple of 3 and 5

rename the fraction 2/5 using tenths and hundredths​

Answers

Answer:

20/50

Step-by-step explanation:

i think

max is thinking of a number which he calls n

Answers

Answer:

what are you trying to ask?

Step-by-step explanation:

7 filler filler filler

Constructing a frequency distribution for grouped data
Ten cyclists were each asked the distance in miles they biked last week.
Their responses are given below.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of distances in that class.
(Note that we are using a class width of 5.)
Distance in miles
Distance in miles
Frequency

3
20
6
3
7
8
13
10
18
12
6 to 10
11 to 15
16 to 20 and 1 to 5

Answers

The grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

Given that, ten cyclists were each asked the distance in miles they biked last week. The distance travelled by 10 cyclists is 3, 20, 6, 3, 7, 8, 13, 10, 18 and 12.

We need to complete the grouped frequency distribution for the data.

What is the grouped frequency distribution?

In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.

Now, the frequency distribution for the given intervals is as follows:

That is, for intervals 1 to 5 the frequency is 2.

For intervals 5 to 10 the frequency is 4.

For intervals 11 to 15 the frequency is 2.

For intervals 16 to 20 the frequency is 2.

Therefore, the grouped frequency distribution for the data with the given intervals is 2, 4, 2 and 2 respectively.

To learn more about the grouped frequency distribution visit:

brainly.com/question/4679134.

#SPJ2

i finished the other question but i need help with this one!!!! I will give brainleist

Answers

Answer:

1.22 meters aprx.

Step-by-step explanation:

This is talking about meters right. If it is 1.22 would be your answer.

Can anyone solve this? If so tell me and make sure u know what ur doing please

Answers

Answer:

-2

Step-by-step explanation:

To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be using the points (-3, 2) and (-1, -2).

[tex]\frac{rise}{run}[/tex] = [tex]\frac{-2-2}{-1-(-3)}[/tex]

     = [tex]\frac{-2-2}{-1+3}[/tex]

     = [tex]\frac{-4}{2}[/tex]

     = -2

There are 2400 students in a school 45% of them are boys how many boys are in the school

Show your work in the answer

Answers

Answer:

1080 boys

Step-by-step explanation:

2400 x 0.45 = 1080

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